User contributions for Joel2

8 July 2024

• 14:4714:47, 8 July 2024 diff hist 0 N File:A21.png No edit summary current
• 14:4514:45, 8 July 2024 diff hist +77,329 N SSC/Stability/BiPolytrope00 Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Radial Oscillations of a Zero-Zero Bipolytrope= This chapter includes the interface-matching condition specified by {{ LW58full }}. It replaces an earlier overview chapter, which summarized models in which an incorrect interface matching condition was used. In a SSC/Structure/BiPolytropes/Analytic00#BiPolytrope_with_nc_.3D_0_and_ne_..." current
• 14:4214:42, 8 July 2024 diff hist +94,388 N SSC/Stability/BiPolytrope00Details Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Searching for Additional Eigenvectors of Zero-Zero Bipolytropes= This chapter is an extension of two accompanying discussions: The original ''discovery'' and detailed derivation; and the more readable, summary. In our SSC/Stability/BiPolytrope00#Radial_..." current
• 14:3914:39, 8 July 2024 diff hist 0 N File:Heaviside01.png No edit summary current
• 14:3814:38, 8 July 2024 diff hist +2,366 N Appendix/Mathematics/StepFunction Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Unit Step Function and Its Derivative= ==Standard Presentation== The unit — or, [https://en.wikipedia.org/wiki/Heaviside_step_function Heaviside] — step function, <math>H(x)</math>, is defined such that, <table border="0" align="center" cellpadding="8"> <tr> <td align="center"> <math> H(x) = \begin{cases} 0; & ~~ x < 0 \\ 1; & ~~ x > 0 \end{cases} </math> <p><br /> [<b>Appendix/References#MF53|<fon..." current
• 14:3114:31, 8 July 2024 diff hist +41,803 N Appendix/Mathematics/ScaleFactors Created page with "__FORCETOC__ <!-- will force the creation of a Table of Contents --> <!-- __NOTOC__ will force TOC off --> =Scale Factors for Orthogonal Curvilinear Coordinate Systems= Here we lean heavily on the class notes and associated references that have been provided by [https://unidirectory.auckland.ac.nz/profile/pa-kelly P. A. Kelly] in a collection titled, ''[http://homepages.engineering.auckland.ac.nz/~pkel015/SolidMechanicsBooks/index.html Mechanics Lecture Notes: An Introd..." current
• 14:2614:26, 8 July 2024 diff hist +150,468 N Appendix/Ramblings/Bordeaux Created page with "__FORCETOC__ <!-- will force the creation of a Table of Contents --> <!-- __NOTOC__ will force TOC off --> =Université de Bordeaux (Part 1)= ==Spheroid-Ring Systems== Through a research collaboration at the [https://www.u-bordeaux.com Université de Bordeaux], [https://ui.adsabs.harvard.edu/abs/2019MNRAS.487.4504B/abstract B. Basillais & J. -M. Huré (2019), MNRAS, 487, 4504-4509] have published a paper titled, ''Rigidly Rotating, Incompressible S..." current
• 14:0814:08, 8 July 2024 diff hist +27,035 N Appendix/Ramblings/BordeauxSequences Created page with "__FORCETOC__ <!-- will force the creation of a Table of Contents --> <!-- __NOTOC__ will force TOC off --> =Université de Bordeaux (Part 2)= ==Exterior Gravitational Potential of Toroids== [https://ui.adsabs.harvard.edu/abs/2020MNRAS.494.5825H/abstract J. -M. Huré, B. Basillais, V. Karas, A. Trova, & O. Semerák (2020), MNRAS, 494, 5825-5838] have published a paper titled, ''The Exterior Gravitational Potential of Toroids.'' Here we examine how..." current
• 14:0714:07, 8 July 2024 diff hist 0 N File:AKM2003Fig2.png No edit summary current
• 14:0614:06, 8 July 2024 diff hist 0 N File:EriguchiHachisu83 Fig3.png No edit summary current
• 14:0514:05, 8 July 2024 diff hist 0 N File:EriguchiSugimoto81Fig1.png No edit summary current
• 13:5613:56, 8 July 2024 diff hist 0 N File:BH2019Fig4.png No edit summary current
• 13:5513:55, 8 July 2024 diff hist 0 N File:HachisuEriguchi1984Fig3modified.png No edit summary current
• 13:5413:54, 8 July 2024 diff hist 0 N File:HachisuEriguchi1984.jpg No edit summary current
• 13:5313:53, 8 July 2024 diff hist +11,544 N Appendix/Ramblings/BordeauxPostDefense Created page with "__FORCETOC__ <!-- will force the creation of a Table of Contents --> <!-- __NOTOC__ will force TOC off --> =Université de Bordeaux (Part 3)= ==Discussions Following Dissertation Defense== ===Shapes=== ====Jean-Marc's Question to Joel Regarding Shapes==== <font color="maroon">When you ask about topological changes around Ansorg's solution, did you mean for instance the change in the shape of the two bodies, with rounded edges, and slightly less oblate spheroid and..."
• 13:5113:51, 8 July 2024 diff hist +2 Appendix/Ramblings/BdHN →Binary-driven Hypernovae current
• 13:4413:44, 8 July 2024 diff hist −17 Appendix/Ramblings/BdHN No edit summary
• 13:4013:40, 8 July 2024 diff hist +35,224 N Appendix/Ramblings/BdHN Created page with "__FORCETOC__ =Binary-driven Hypernovae= The material presented here builds on our separate discussion of close binary stars. HIDDEN as of 4 July 2023. <!-- BEGIN HIDDEN (pt. 1) ==Setup== ===Initial Carbon-Oxygen Core=== <span id="MPT77angmom">The</span> total angular momentum associated with a Maclaurin spheroid of eccentricity, <m..."
• 13:2913:29, 8 July 2024 diff hist +18,575 N MathProjects/EigenvalueProblemN1 Created page with "__FORCETOC__ =Find Analytic Solutions to an Eigenvalue Problem= <font color="red">'''Note from J. E. Tohline to Students with Good Mathematical Skills'''</font>: This is one of a set of well-defined research problems that are being posed, in the context of this online H_Book, as challenges to young, applied mathematicians. The astronomy community's understanding of the ''Structure, Stability, and Dynamics'' of stars a..." current
• 13:2813:28, 8 July 2024 diff hist +2,385 N Appendix/Ramblings/ForPJinApril2021 Created page with "__FORCETOC__ <!-- will force the creation of a Table of Contents --> <!-- __NOTOC__ will force TOC off --> =For Pranav Jadhav in April 2021= ==Potentially Relevant Initial Links== * Tiled Menu * Fission Hypothesis of Binary Star Formation * ThreeDimensionalConfigurations/ChallengesPt2#COLLADA-Based_Representation|COLLADA-based Representation of..." current

7 July 2024

• 15:5115:51, 7 July 2024 diff hist +8,064 N Appendix/Ramblings/ForPaulFisher Created page with "__FORCETOC__ <!-- will force the creation of a Table of Contents --> <!-- __NOTOC__ will force TOC off --> =For Paul Fisher= ==Overview of Dissertation== [https://digitalcommons.lsu.edu/gradschool_disstheses/6940/ Paul Fisher's (1999) doctoral dissertation] (accessible via the LSU Digital Commons) is titled, ''Nonaxisymmetric Equilibrium Models for Gaseous Galaxy Disks.'' Its abstract reads, in part: <table border="0" align="center" width="80%" cellpadding="3"><tr><t..." current
• 15:4515:45, 7 July 2024 diff hist +132 Appendix/Ramblings/ForDurisen →For Richard H. Durisen current
• 15:3815:38, 7 July 2024 diff hist +4,417 N Appendix/Ramblings/ForDurisen Created page with "<!-- __FORCETOC__ will force the creation of a Table of Contents --> <!-- __NOTOC__ will force TOC off --> =For Richard H. Durisen= ==Highlights Mentioned on 1 March 2020== <ul> <li><font size="+1">Tiled Menu:</font>  Most ''tiles'' presented on this ''menu'' page contain a short title that is linked to a hypertext-enhanced chapter where you can find a technical discussion of the identified topic. Have fun reading any one of thes..."

6 July 2024

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• 19:3219:32, 6 July 2024 diff hist −4 Appendix/Ramblings/PatrickMotl →Initial Comments current
• 19:3119:31, 6 July 2024 diff hist +16 Appendix/Ramblings/PatrickMotl →Initial Comments
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5 July 2024

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• 19:5319:53, 5 July 2024 diff hist 0 N File:FramedDissertationMosaic02HalfAnnotatedSm.png No edit summary current
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• 19:5019:50, 5 July 2024 diff hist +48,036 N Appendix/Ramblings/MyDoctoralStudents Created page with "__FORCETOC__ <!-- __FORCETOC__ will force the creation of a Table of Contents --> <!-- __NOTOC__ will force TOC off --> =Chronology of Research Endeavors= ==Preface== Looking back, it seems clear to me that the technical book that has had the most influence on my research career has been [<b><font color="red">EFE</font></b>], that is, Chandrasekhar's (originally, 1969) ''Ellipsoidal Figures of Equilibrium.'' Chandrasekhar evaluated the relat..." current
• 19:4819:48, 5 July 2024 diff hist +3,187 N Appendix/Ramblings/InsideOut Created page with "__FORCETOC__ <!-- will force the creation of a Table of Contents --> <!-- __NOTOC__ will force TOC off --> =Looking Outward, From Inside a Black Hole= [Written by J. E. Tohline, early morning of 13 October 2017]  The relationship between the mass, <math>~M</math>, and radius, <math>~R</math>, of a black hole is, <div align="center"> <table border="0" cellpadding="5" align="center"> <tr> <td align="right"> <math>~\frac{2GM}{c^2 R}</math> </td> <td align="cent..." current
• 19:4619:46, 5 July 2024 diff hist −13 Appendix/Ramblings/LedouxVariationalPrinciple →Application to n = 5 Polytropic Configuration current
• 19:4519:45, 5 July 2024 diff hist −13 Appendix/Ramblings/LedouxVariationalPrinciple →Known Analytic Eigenfunction
• 19:4419:44, 5 July 2024 diff hist −95 Appendix/Ramblings/LedouxVariationalPrinciple →LP41 Again
• 19:3819:38, 5 July 2024 diff hist −39 Appendix/Ramblings/LedouxVariationalPrinciple →Review by Ledoux and Walraven (1958)
• 19:3719:37, 5 July 2024 diff hist −13 Appendix/Ramblings/LedouxVariationalPrinciple →Ledoux's Variational Principle (Supporting Derivations)
• 19:3619:36, 5 July 2024 diff hist +47,841 N Appendix/Ramblings/LedouxVariationalPrinciple Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Ledoux's Variational Principle (Supporting Derivations)= An accompanying chapter presents a summary discussion of Ledoux's variational principle, emphasizing how it relates to stability analyses that are built upon free-energy arguments. The detailed derivations presented below provide the foundation upon which that summary discussion has bee..."